When Is Information Sufficient for Action? Search with Unreliable yet Informative Intelligence

Abstract

We analyze a variant of the whereabouts search problem, in which a searcher looks for a target hiding in one of n possible locations. Unlike in the classic version, our searcher does not pursue the target by actively moving from one location to the next. Instead, the searcher receives a stream of intelligence about the location of the target. At any time, the searcher can engage the location he thinks contains the target or wait for more intelligence. The searcher incurs costs when he engages the wrong location, based on insufficient intelligence, or waits too long in the hopes of gaining better situational awareness, which allows the target to either execute his plot or disappear. We formulate the searcher's decision as an optimal stopping problem and establish conditions for optimally executing this search-and-interdict mission.

Timely exposure of a secret project: Which activities to monitor?

“…Building on the model of Pinker et al (2013), one could assign a detection weight to each task and assume that discovery occurs if the total weight of detected tasks exceeds a given threshold. In line with the article of Atkinson et al (Atkinson et al, 2016), an important question then arises: how much evidence should the defender collect before engaging? An additional concern is how to deal with false-positive detections.…”

“…Atkinson and Wein (2010) examine how a government should allocate its resources over the inspection of terror and criminal networks to exploit the finding of Smith, Damphousse, and Roberts (2006) that, prior to an attack, terrorists frequently participate in crimes such as theft or procuring explosives. Other articles address problems such as predicting the number of undetected terror threats (Kaplan, 2010), estimating the duration of a terrorist plot (Kaplan, 2012a), locating terrorists (Alpern & Lidbetter, 2013;Atkinson, Kress, & Lange, 2016), processing intelligence (Dimitrov, Kress, & Nevo, 2016;Lin, Kress, & Szechtman, 2009), patrolling an area (Lin, Atkinson, & Glazebrook, 2014;Papadaki, Alpern, Lidbetter, & Morton, 2016;Szechtman, Kress, Lin, & Cfir, 2008), and predicting the goal of a suspected terrorist (Tsitsiklis & Xu, 2018). In particular, Atkinson et al (2016) consider a searcher who, based on a stream of unreliable intelligence about a target's location, needs to decide whether to engage or to wait for more information.…”

Opportunistic Advertisement Scheduling in Live Social Media: A Multiple Stopping Time POMDP Approach

“…It can be easily checked the parametrization in (23) satisfies the conditions in Theorem 2 and Theorem 3.…”

“…However, in this paper we deal with sequential scheduling in a partially observed case. [22], [23] consider an optimal search problem where the searcher receives imperfect information on a (static) target location and decides optimally to search or interdict by solving a classical optimal stopping problem (L = 1). However, the multiple-stopping problem considered in this paper is equivalent to a search problem where the underlying process is evolving (Markovian) and the searcher needs to optimally stop L > 1 times to achieve a specific objective.…”

Designing Risk‐Adjusted Therapy for Patients with Hypertension

“…Therefore, further restrictions, such as considering binary decisions (Chao and Kavadias 2008) and binary types (Kavadias and Loch 2003) in dynamic R&D project selection, are added to the model to make its analysis tractable. Finally, thanks to their ease of interpretation and practicality, control-limit type policies have found applications in other sequential irreversible decision problems in OM that deal with "when to enter a market" Uncu 2013, 2015), "when to stop searching" (Atkinson et al 2016, Harrison and Sunar 2015, Palley and Kremer 2014, "when to stop acquiring new/advanced demand information" (Boyacı and € Ozer 2010, Ding et al 2014, Rahmani et al 2017, etc. We refer readers to Oh and € Ozer (2016) for a recent treatment of optimal stopping problems.…”